Inducing high exo selectivity in Diels–Alder reaction by dimethylborane substituent: a DFT study

In this work, the role of Lewis acid–base (LAB) interaction on the stereoselectivity of the Diels–Alder (DA) reaction has been studied by DFT in gas and solution (dichloromethane) phases. The calculations were performed at the B3LYP/6-311G++ (d, p) level. Two different series of DA reactions were investigated: (1)—three mono-substituted cyclopentadienes + dimethyl(vinyl)borane; (2)—five α,β-unsaturated carbonyl compounds + cyclopenta-2,4-dien-1-yldimethylborane. The reacting diene and dienophile pairs were chosen to restrict LAB interaction to the exo reaction pathway. It was found that in some of the examined cases, the favorable LAB interaction is so strong that it can lead to a completely exo-selective DA reaction. Furthermore, a novel multistep synthetic method was hypothesized for preparing exo cycloadduct with near 100% stereoselectivity. Our results can open up new avenues toward the rational design of exo-selective DA reactions for synthesizing novel bioorganic compounds.

Furthermore, similar series of DA reactions have been successfully employed in our previous work to investigate the role of hydrogen bonding on the stereoselectivity of DA reaction. 31 DFT calculations provided the optimized structures of the transition states (TSs) and final products in the gas and solution phases (dichloromethane). To further explore the kinetics and thermodynamics of the DA reactions, Gibbs free energies of activation and reaction were computed. It was found that the rationally engineered intermolecular LAB interaction can drastically affect the stereoselectivity of the DA reaction leading to almost complete exo selectivity.

Results and discussion
Two series of DA reactions were devised to explore how the stereoselectivity is affected by the LAB interaction. As noted before, the reactants were chosen to restrict the favorable LAB interaction (between the BMe 2 group from one molecule and the lone pair donor atom X from the other) to the exo pathway. The optimized structures of the TSs and final products and their associated Gibbs free energies were acquired for each DA reaction. Also, the B…X distances in exo TS and the final product (denoted as r(B…X, exo)) were evaluated as a measure of the strength of LAB interaction.
Along the reaction path (prior to the TS) in a bimolecular reaction, the two reactants may form a molecular complex (MC) in which they are held together by weak intermolecular interactions such as van der Waals (vdW) forces, hydrogen bonding, and LAB interaction [32][33][34][35][36] . If the resulting MC is less stable than the corresponding free reactants (that is, the standard Gibbs free energy change associated with the formation of MC from the reactants is + 3 kcal/mol or higher), then its equilibrium concentration would be much lower than the reactants (< 1% at room temperature) and thus the formation of MC can be practically ignored. Consequently, free reactants can be used as the energy reference, as usual. On the other hand, if the MC is more stable than the free reactants (that is, the standard Gibbs free energy change corresponding to the formation of MC from the reactants is − 3 kcal/ mol or lower), the equilibrium concentration of the free reactants would be negligible compared to the MC (< 1% at room temperature). Therefore, taking the MC as the energy reference would be necessary. In light of the discussion above, the optimized structure of the MC associated with the reacting diene and dienophile was obtained for each DA reaction. Then, based on the relative stability of the reactants and the MC, the energy reference was determined.
First series of DA reactions. The first series of DA reactions investigated were between the four monosubstituted cyclopentadienes and dimethyl(vinyl)borane (Fig. 1). The optimized structure of the reactants, MCs, TSs, and final products were obtained for each of the three DA reactions.
Our calculations revealed that the MCs for entries 1-1 to 1-2 were 6.40 and 8.85 kcal/mol higher in Gibbs free energy than the reactants, respectively. However, the Gibbs free energy of 1-3 MC was 5.04 kcal/mol lower than the reactants. Consequently, the energy references for entries 1-1 and 1-2 were the free reactants, whereas for entry 1-3, the corresponding MC was chosen as the energy reference. Figure S1  where k exo and k endo are the bimolecular rate constants corresponding to exo and endo reaction pathways, respectively (which can be obtained by the Arrhenius equation), R is the gas constant, and T is the absolute temperature. Table 1 summarizes the results of calculations on TS structures. As can be seen, G • ‡ values for entries 1-1 to 1-3 are − 0.93, − 4.62, and − 6.61 kcal/mol, respectively. The corresponding exo selectivities at 298.15 K calculated from Eqs. (1) and (2) are 82.7, > 99.9, and > 99.9%, respectively. These results show that the exo selectivity increases in the order of X = OH − < NH 2 < CO 2 − . Interestingly, as shown in Table 1, r(B…X, exo) increases in the opposite order. Furthermore, r(B…X, exo) for entries 1-2 and 1-3 are shorter than the sum of the ×100= k exo k exo + k endo ×100= 100   37 . These findings imply that the strength of the LAB interaction between B and X in the exo TS is critical in determining the exo selectivity. In particular, the exo selectivities close to 100% obtained for entries 1-2 and 1-3 are presumably related to the strong B…N and B…O interactions in the TS structures, respectively. Table 2 provides the computation results corresponding to the final products. The difference between the exo and endo standard Gibbs free energies of reaction ( represents the relative thermodynamic stability of exo and endo stereoisomers. It can be observed that G • values for entries 1-1 to 1-3 are − 2.31, − 8.02, and − 26.20 kcal/mol, respectively. Thus, the relative stability of the exo stereoisomer increases in the order of X = OH − < NH 2 < CO 2 − . However, the increase of r(B…X, exo) shows an opposite trend. Moreover, r(B…X, exo) for entries 1-2 and 1-3 are shorter than the sum of the van der Waals radii of B and X. As one can see, these trends are very similar to those observed for TSs. Hence, it can be inferred that G • is primarily affected by the strength of the LAB interaction of B and X. Especially the fairly large absolute values of G • (> 8 kcal/mol) for entries 1-2 and 1-3 are presumably the results of strong B…N and B…O interactions in the final products, respectively.
The reaction energy diagram for entry 1-2 is shown in Fig. 2 as a representative example. Figure 3 depicts the optimized structures of the associated TSs and final products. Table 1. Results of the DFT calculations on the TSs of the three DA reactions outlined in Fig. 1.  Table 2. Results of the DFT calculations on the final products of the three DA reactions outlined in Fig. 1. www.nature.com/scientificreports/ These findings indicate that the exo stereoisomer is the kinetically and thermodynamically dominant product for entries 1-2 and 1-3 due to the strong LAB interaction.
MCs for entries 2-1 to 2-3 were calculated to be 23.40, 5.93, and 8.83 kcal/mol lower in Gibbs free energy than the reactants, respectively. On the other hand, for entries 2-4 and 2-5, MCs were 15.07 and 6.63 kcal/mol higher in Gibbs free energy than the corresponding reactants, respectively. Accordingly, the energy references for entries 2-1 to 2-3 were the reactants, while MCs were taken as the energy references for entries 2-4 and 2-5. Figure S2 shows the optimized structures of the five MCs.  The results of calculations on TSs are given in Table 3. As can be seen, G • ‡ for entries 2-1 to 2-5 are − 10.81, − 11.26, − 0.86, − 26.30, and − 9.09, respectively. The corresponding exo selectivities at 298.15 K are > 99.9, > 99.9, 81.1, > 99.9, and > 99.9%, respectively. Consequently, the exo selectivity increases in the order of X = OH < NH 2 < H < Me < O − . As shown in Table 3, r(B…O, exo) values exhibit an opposite trend. As previously discussed, these observations suggest that the strength of LAB interaction between B (from the diene) and O of the carbonyl is the primary factor in determining the exo selectivity. Furthermore, the much higher G • ‡ absolute values compared to the first series of DA reactions (entries 1-1 to 1-3) imply stronger LAB interactions. Table 4 shows the calculation results corresponding to the final products, in which G • values for entries 2-1 to 2-5 are 1.33, − 5.04, 0.97, − 25.74, and − 2.94 kcal/mol, respectively. Thus, the absolute value of G • increases in the order of X = H < OH − < NH 2 < Me < O − . According to Table 4, this order is almost reversed for Table 3. Results of the DFT calculations on the TSs of the five DA reactions outlined in Fig. 4.  The reaction energy diagram for entry 2-2 is given in Fig. 5 as a representative example. Figure 6 illustrates the optimized structures of the associated TSs and final products.
Overall, the data in Tables 3 and 4 clearly demonstrate that the exo stereoisomer is the dominant kinetic and thermodynamic product for entries 2-2, 2-4, and 2-5 due to the strong LAB interaction.

Solution-phase calculations.
To complement the gas phase calculations discussed in previous sections, solution-phase calculations in dichloromethane (DCM) were performed on MCs, reactants, TSs, and final products of the two series of DA reactions. It should be noted that the optimized structures in DCM were assumed to be the same as those obtained in the gas phase since the energy differences were negligible. Our calculations indicated that MCs for entries 1-1 to 1-3 were 8.88, 7.66, and 6.92 kcal/mol higher in Gibbs free energy than the reactants, respectively. For entries 2-1 to 2-4, MCs were 28.83, 22.67, 11.36, and 2.14 kcal/mol higher in Gibbs free energy than the reactants, respectively. However, for entry 2-5, MC was 4.95 kcal/mol lower in Gibbs free energy than the reactants. Consequently, the reactants were chosen as the energy reference for entries 1-1 to 1-3 and 2-1 to 2-4, whereas for entry 2-5, MC was chosen as the energy reference. Tables 5 and 6 summarize The results of calculations on the final products of the first and second series of DA reactions are shown in Tables 7 and 8, respectively. Again, the observed trend in G • is similar to that of the gas phase for both series of DA reactions. Moreover, G • values in solution are roughly similar to those in the gas phase (except for entries 1-3 and 2-4).
Overall, solvent calculations indicated that the trend in gas-phase exo selectivities is mainly preserved in DCM, even though the gas-phase G • ‡ and G • absolute values were smaller than those in DCM.
A novel synthetic strategy for preparing exo cycloadducts. Based on the findings of this study, a synthetic strategy has been proposed for preparing stereochemically-pure exo cycloadducts. As depicted in Fig. 7, the first step is the DA reaction of an α,β-unsaturated carbonyl compound and cyclopenta-2,4-dien-1-yldimethylborane, which yields almost exclusively the exo stereoisomer (according to our calculations). The next step involves the reduction of carbonyl to CH 2 , which can be performed with high yield and under mild conditions with a variety of methods such as Et 3 SiH + catalytic amounts of B(C 6 F 5 ) 3

38
, polymethylhydrosiloxane + catalytic amounts of B(C 6 F 5 ) 3 , 39 and ruthenium (II)-catalyzed Wolf-Kishner reaction 40 . In the third step, Table 5. Results of the solution-phase DFT calculations on the TSs of the three DA reactions outlined in Fig. 1.  Table 7. Results of the solution-phase DFT calculations on the final products of the three DA reactions outlined in Fig. 1.    41,42 . This is the second step of the well-known hydroboration-oxidation reaction, which transforms an alkene into alcohol.
(3)-Reduction of the ketone to CH 2 by the mild and efficient methods described above (step 6).

Conclusions
A series of dienes and dienophiles were designed to theoretically examine the role of intermolecular LAB interaction on the stereoselectivity of DA reaction. DFT calculations revealed that the favorable interaction between the BMe 2 group (LA) of one reactant and the lone-pair donor atom (LB) of the other reactant could significantly affect the stereoselectivity of the DA reaction. Remarkably, when the LAB interaction is strong enough, it can lead to a completely exo-selective DA reaction in the gas and solution phases. Inspired by these results, a novel method was proposed to synthesize stereochemically pure exo-2-alkylbicyclo[2.2.1]heptanes. Our findings can provide new insights into the rational design of exo-selective DA reactions.

Methods
Density functional theory (DFT) was employed to calculate the molecular structures and energies. First, the conformers with the lowest energy were found at the relative energy of 0-10 kcal/mol range for the reaction components using the Merck Molecular Force field (MMFF) in Spartan 14 software 43 . Then, the most stable conformers were optimized by the DFT calculations at the B3LYP/6-311++ G (d, p) computational level [44][45][46] , in which "p" and "d" denote polarized and diffuse functions, respectively. The diffuse function is vital for molecules with lone pairs and anions [47][48][49] . We have justified the use of MMFF and B3LYP computational levels in our previous works 50,51 . Since the energy ordering might vary between MMFF and DFT, DFT optimization was performed on the lowest energy MMFF conformers at the relative energy range of 1-3 kcal/mol. The lack of imaginary frequencies verified the existence of the local energy minima of the structures under consideration. The solution-phase calculations were performed using the conductor-like polarizable continuum model (CPCM) 52,53 . All calculations were carried out at 1.00 atm and 298.15 K.

Data availability
All data generated or analyzed during this study are included in this published article [and its supplementary information files].